# Is the maximum possible bandwidth of a radar system dependent (or related) to its center frequency?

One of the core parameters of any radar system is its center frequency. Another core parameter is its bandwidth, which is the reciprocal of its ranging resolution. I am wondering: Is there some sort of dependence or relationship between those two? Naively, I would say that the higher the center frequency, the higher also the bandwidth can be. But is that true, and if so, why is that so?

• you're not referring to any radar system, but the large class of pulse radars (whether or not they use pulse compression), but, honestly: make a plot of a power spectrum, say from 0 Hz to 20 GHz. Draw in a vertical line mark a carrier frequency at 2 GHz. Can you put a bandwidth of 5 GHz around that? Does that answer your question? Commented Jan 12, 2023 at 11:14
• So you're saying these considerations are different for, say, FMCW radars? Commented Jan 12, 2023 at 13:31
• ha, that's a good question, but for range purposes, the chirp bandwidth of FMCW is not as important Commented Jan 12, 2023 at 16:08
• By "center frequency" are you referring to the RF carrier? Commented Jan 13, 2023 at 7:19
• @Michael The answer I posted below applies to any type of radar system. There are some exotic antennas that mitigate this effect but come with other trade-offs and aren't used that often relatively speaking. Commented Jan 16, 2023 at 15:01

I'm assuming you're referring to the RF carrier frequency and not some intermediate frequency (IF), or even baseband where the center frequency can be zero.

Your intuition that there is a meaningful relationship between the carrier and bandwidth is correct, and one main example is what is called the fractional bandwidth (FBW) of an antenna. The ratio is given by

$$FBW = \frac{f_2 - f_1}{f_c}$$

Where $$f_1$$ and $$f_2$$ are the lower and upper frequencies centered around $$f_c$$.

When defining an array, one usually defines the antenna for a single frequency and yields the usual pattern you've probably seen before.

Let's take two 16-element arrays whose center frequencies $$f_c$$ are at 2 GHz and 10 GHz respectively. Both will have an element spacing of $$0.5\lambda$$.

## Narrowband Operation

Now let's assume we're transmitting a waveform with 5 MHz bandwidth $$B$$. Also we want to steer the array to 30 degrees off-boresight.

The antenna patterns for the three frequencies $$f_c-B/2$$, $$f_c$$, $$f_c+B/2$$ at the desired steering angle are

You can see that since the waveform has such a narrow bandwidth, the traditional phase-shift steering of the array yields the same pattern over all of the frequencies.

## Wideband Operation

Now the issue is when we have a wideband waveform, let's say 500 MHz:

Now, the steering angle of the 2 GHz array now changes significantly as a function of frequency. The 10 GHz array is more robust to this because the FBW is smaller. That is, the minimum and maximum frequencies to be transmitted/received by the array are relatively close $$f_c$$ and thus the array "looks more similar" at all frequencies as opposed to the 2 GHz array.

## Effects of High FBW

The 2 GHz and 10 GHz arrays have FBWs of 25% and 5%, respectively. This metric clues you in on how well the array will behave given a certain bandwidth. In our case, the 2 GHz array will have issues using the 500 MHz waveform when compared to the other. To your particular question, using a higher $$f_c$$ allows you to push higher bandwidths while mitigating these effects. Thus, the relationship between the center frequency and the desired bandwidth absolutely affects the system design!

• I assume that does not only hold for arrays, but also in a similar way for a simple radar with just a single transmit/receive antenna? Commented Jan 15, 2023 at 8:26
• @Michael That's right. I just used a simple array to show the effect of electronically steering a beam where the effect is more pronounced. The same effect occurs in other antennas since the beam pattern changes with frequency. As a matter of fact, some radar systems exploited this fact to achieve electronic steering by simply changing frequencies. Commented Jan 15, 2023 at 15:37
• @Michael Mind you, there are various techniques to mitigate these effects, such as the various wideband beamformers. Commented Jan 17, 2023 at 19:41
• well, I am not so much interested in mitigating these effects in array SARs. I was really only just wondering, if you design a SAR system, how would you choose the bandwidth? Of course based on resolution requirements, but there had to be other limiting factors. Apparently one is the relationship to the center frequency. Commented Jan 19, 2023 at 6:39